Electric Power Problems

1. It's a cool day, about 10 oC, so you plan to make about 5.0 kg of clear soup using your slow cooking crockpot. To decide whether the soup will be ready for dinner, you estimate how long it will take before the soup gets to its boiling point. Before adding the ingredients, you turn the crockpot over and read that it is a 200-ohm device that operates at 120 volts. Since your soup is mostly water, you assume it has the same thermal properties as water, so its specific heat capacity is 4200 J/(kg oC) and its heat of vaporization is 2.3 x 106 J/kg.
   
   
2. You are working with a company that has the contract to design a new, 700-foot high, 50-story office building in Minneapolis. Your boss suddenly bursts into your office. She has been talking with an engineer who told her that when the elevator is operating at maximum speed, it would take the 6500-lb loaded elevator one minute to rise 20 stories. She thinks this is too long a time for these busy executives to spend in an elevator after returning from lunch at the Minneapolis Athletic Club. She wants you to buy a bigger power supply for the elevator. You look up the specifications for the new supply and find that it is the same as the old one except that it operates at twice the voltage. Your boss's assistant argues that the operating expenses of the new power supply will be much more than the old one. Your boss wants you to determine if this is correct. You estimate that while the elevator runs at maximum speed, the whole system, including the power supply, is 60% efficient. The cost of electricity is $0.06 per kilowatt-hour (commercial rate).
   
   
3. You have finally graduated from college and found a job with the Washington State Agricultural Concerns Group. Farmers and fishermen are concerned that the rate that water flows in the Columbia river, which is controlled by dams, will not be adequate for both irrigation needs and salmon spawning. The dams control the river's flow rate to produce most of the electrical power for cities along the West Coast. Your group leader assigns you the task of calculating the volume of water per second (flow rate) which normally would flow through the Grand Coulee Dam, the largest on the Columbia River. She tells you that this dam typically generates 2000 megawatts (MW) of power and is 50% efficient in converting the water's energy to electrical energy. The dam is 170 meters high ,and the water is kept in a lake 10 meters below the top of the dam. The Columbia River is 170 meters wide at the dam. The density of water is 1.00 g/cm3.